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Shareholders' Deficit - Additional Information (Detail) (USD $)
0 Months Ended 12 Months Ended 0 Months Ended
Nov. 01, 2012
Oct. 31, 2012
Mar. 09, 2012
Feb. 28, 2012
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
May 14, 2014
Nov. 10, 2014
May 28, 2014
May 27, 2014
Oct. 30, 2013
Class of Stock [Line Items]                        
Common stock issued         124,129,000us-gaap_CommonStockSharesIssued 129,652,000us-gaap_CommonStockSharesIssued            
Proceeds from issue of common stock through IPO           $ 525,000,000us-gaap_ProceedsFromIssuanceOfCommonStock $ 3,116,000us-gaap_ProceedsFromIssuanceOfCommonStock          
Preferred stock, authorized         1,000,000us-gaap_PreferredStockSharesAuthorized              
Preferred stock, par value         $ 0.01us-gaap_PreferredStockParOrStatedValuePerShare              
Preferred stock, shares issued         0us-gaap_PreferredStockSharesIssued 0us-gaap_PreferredStockSharesIssued            
Equity repurchase program authorized amount                       125,000,000us-gaap_StockRepurchaseProgramAuthorizedAmount1
Repurchases under the equity repurchase program           65,500,000us-gaap_StockRepurchasedAndRetiredDuringPeriodValue            
Repurchase of common stock, Shares         7,591,175us-gaap_StockRepurchasedDuringPeriodShares 153,223us-gaap_StockRepurchasedDuringPeriodShares 508,656us-gaap_StockRepurchasedDuringPeriodShares          
Repurchase of common stock, value         415,131,000us-gaap_StockRepurchasedDuringPeriodValue 6,434,000us-gaap_StockRepurchasedDuringPeriodValue 13,363,000us-gaap_StockRepurchasedDuringPeriodValue          
Common stock repurchased, average share price           $ 42.01q_ShareRepurchasesPricePaidPerShare            
Credit facility amount used to fund repurchase         0us-gaap_LineOfCredit 0us-gaap_LineOfCredit            
Dividend declared per share   $ 2.09us-gaap_CommonStockDividendsPerShareCashPaid   $ 2.82us-gaap_CommonStockDividendsPerShareCashPaid                
Dividend, date declared   2012-10   2012-02                
Dividend, date of record   Oct. 24, 2012   Feb. 29, 2012                
Dividend, date to be paid   Nov. 01, 2012   Mar. 29, 2012                
Total dividend paid 241,700,000us-gaap_Dividends   326,100,000us-gaap_Dividends                  
Revolving credit facility [Member]                        
Class of Stock [Line Items]                        
Credit facility amount used to fund repurchase         150,000,000us-gaap_LineOfCredit
/ us-gaap_CreditFacilityAxis
= us-gaap_RevolvingCreditFacilityMember
             
IPO [Member]                        
Class of Stock [Line Items]                        
Common stock price               $ 40.00us-gaap_SharePrice
/ us-gaap_SubsidiarySaleOfStockAxis
= us-gaap_IPOMember
       
Common stock issued               13,125,000us-gaap_CommonStockSharesIssued
/ us-gaap_SubsidiarySaleOfStockAxis
= us-gaap_IPOMember
       
Proceeds from issue of common stock through IPO               489,500,000us-gaap_ProceedsFromIssuanceOfCommonStock
/ us-gaap_SubsidiarySaleOfStockAxis
= us-gaap_IPOMember
       
Selling Shareholders [Member] | IPO [Member]                        
Class of Stock [Line Items]                        
Sale of common stock               14,111,841q_CommonStockSharesOfferedAndSoldByShareholders
/ us-gaap_StatementEquityComponentsAxis
= q_SellingShareholdersMember
/ us-gaap_SubsidiarySaleOfStockAxis
= us-gaap_IPOMember
       
Proceeds from issue of common stock through IPO               0us-gaap_ProceedsFromIssuanceOfCommonStock
/ us-gaap_StatementEquityComponentsAxis
= q_SellingShareholdersMember
/ us-gaap_SubsidiarySaleOfStockAxis
= us-gaap_IPOMember
       
Selling Shareholders [Member] | IPO [Member] | Underwriters Option [Member]                        
Class of Stock [Line Items]                        
Shares offered and sold by selling shareholders pursuant to the full exercise of the underwriters' option to purchase additional shares               3,552,631q_CommonStockSharesOfferedAndSoldBySellingShareholders
/ us-gaap_OptionIndexedToIssuersEquityTypeAxis
= q_UnderwritersOptionMember
/ us-gaap_StatementEquityComponentsAxis
= q_SellingShareholdersMember
/ us-gaap_SubsidiarySaleOfStockAxis
= us-gaap_IPOMember
       
Stock Options [Member]                        
Class of Stock [Line Items]                        
Equity repurchased -vested in-the-money employee stock options, shares           2,000,000q_RepurchaseOfVestedInMoneyStockOptions
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_EmployeeStockOptionMember
           
Equity repurchased -vested in-the-money employee stock options, value           59,100,000q_RepurchaseOfVestedInMoneyStockOptionsValue
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_EmployeeStockOptionMember
           
Repurchase vested in-the-money employee stock options, average market price           $ 43.42us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPerShareWeightedAveragePriceOfSharesPurchased
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_EmployeeStockOptionMember
           
Repurchase of vested in-the-money employee stock options, average exercise price per option           $ 13.74us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_EmployeeStockOptionMember
           
Other Equity Repurchases [Member]                        
Class of Stock [Line Items]                        
Repurchase of common stock, Shares                 4,303,666us-gaap_StockRepurchasedDuringPeriodShares
/ us-gaap_ShareRepurchaseProgramAxis
= q_OtherEquityRepurchasesMember
3,287,209us-gaap_StockRepurchasedDuringPeriodShares
/ us-gaap_ShareRepurchaseProgramAxis
= q_OtherEquityRepurchasesMember
   
Repurchase of common stock, value                 250,000,000us-gaap_StockRepurchasedDuringPeriodValue
/ us-gaap_ShareRepurchaseProgramAxis
= q_OtherEquityRepurchasesMember
165,100,000us-gaap_StockRepurchasedDuringPeriodValue
/ us-gaap_ShareRepurchaseProgramAxis
= q_OtherEquityRepurchasesMember
   
Repurchase of common stock, share price                 $ 58.09q_StockRepurchasedDuringPeriodPerShare
/ us-gaap_ShareRepurchaseProgramAxis
= q_OtherEquityRepurchasesMember
$ 50.23q_StockRepurchasedDuringPeriodPerShare
/ us-gaap_ShareRepurchaseProgramAxis
= q_OtherEquityRepurchasesMember
$ 51.26q_StockRepurchasedDuringPeriodPerShare
/ us-gaap_ShareRepurchaseProgramAxis
= q_OtherEquityRepurchasesMember
 
Repurchase price per share percentage                     98.00%q_PercentageOfRepurchasePriceToCurrentStockPrice
/ us-gaap_ShareRepurchaseProgramAxis
= q_OtherEquityRepurchasesMember
 
Other Equity Repurchases [Member] | Revolving credit facility [Member]                        
Class of Stock [Line Items]                        
Credit facility amount used to fund repurchase                 150,000,000us-gaap_LineOfCredit
/ us-gaap_CreditFacilityAxis
= us-gaap_RevolvingCreditFacilityMember
/ us-gaap_ShareRepurchaseProgramAxis
= q_OtherEquityRepurchasesMember
     
Share Repurchase Program [Member]                        
Class of Stock [Line Items]                        
Repurchase of common stock, Shares         300us-gaap_StockRepurchasedDuringPeriodShares
/ us-gaap_ShareRepurchaseProgramAxis
= q_ShareRepurchaseProgramMember
             
Repurchase of common stock, value         14,000us-gaap_StockRepurchasedDuringPeriodValue
/ us-gaap_ShareRepurchaseProgramAxis
= q_ShareRepurchaseProgramMember
             
Repurchase of common stock, share price         $ 47.51q_StockRepurchasedDuringPeriodPerShare
/ us-gaap_ShareRepurchaseProgramAxis
= q_ShareRepurchaseProgramMember
             
Equity available for repurchase under the repurchase program         $ 59,500,000us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1
/ us-gaap_ShareRepurchaseProgramAxis
= q_ShareRepurchaseProgramMember